Question

'n' moles of an ideal gas at temperature \(\mathrm{T}\) (in Kelvin) occupy ' \(\mathrm{V}\) ' litres of volume, exerting a pressure of ' \(\mathrm{P}\) ' atomospheres. What is its concentration (in \(\mathrm{mol} \mathrm{L}^{-1}\) )? \((\mathrm{R}=\) gas constant \():\) (a) \(\mathrm{P} / \mathrm{RT}\) (b) \(\mathrm{PT} / \mathrm{R}\) (c) \(\mathrm{RT} / \mathrm{P}\) (d) \(\mathrm{R} / \mathrm{PT}\)

Short answer

The concentration is \( \frac{P}{RT} \), so option (a) is correct.

Step-by-step solution

Recall the Ideal Gas Law

The ideal gas law is given by the formula: \( PV = nRT \), where \( P \) is the pressure in atmospheres, \( V \) is the volume in liters, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

Define Concentration

Concentration is defined as the number of moles \( n \) of a substance per unit volume \( V \) and is expressed as \( \frac{n}{V} \) in moles per liter (\( \text{mol/L} \)).

Rearrange the Ideal Gas Law

From the ideal gas law \( PV = nRT \), solve for \( \frac{n}{V} \) (concentration) by dividing both sides of the equation by \( V \): \[ \frac{n}{V} = \frac{P}{RT} \]

Compare with Options

Check the given options against the expression derived from the ideal gas law for concentration: - (a) \( \frac{P}{RT} \) which matches our derived formula.- (b) \( \frac{PT}{R} \) which does not match.- (c) \( \frac{RT}{P} \) which does not match.- (d) \( \frac{R}{PT} \) which does not match.

Key concepts

Mole Concept

The mole concept is a fundamental principle in chemistry that helps us express amounts of a chemical substance. One mole of any substance contains Avogadro's number of entities, which is approximately \(6.022 \times 10^{23}\) particles. This huge number is used to easily relate quantities of atoms, molecules, or ions.
Understanding moles is essential when dealing with reactions and properties of substances. When you talk about an "amount" in chemistry, it often refers to moles, providing a bridge between the atomic scale and the macroscopic world we observe.

- **In the context of gases**, moles allow us to explore relationships between volume, pressure, and temperature using the Ideal Gas Law.
- **For solutions**, moles help determine concentration, expressing how much solute is present in a given volume of solvent.

With the Ideal Gas Law task, calculating the number of moles \( n \) using other properties like pressure, temperature, and volume, allows us to determine the concentration of the gas.

Gas Laws

Gas laws describe how gases behave with respect to volume, temperature, and pressure. These laws provide a foundation for predicting how a gas will react under different conditions. A key law is the Ideal Gas Law, expressed as \( PV = nRT \). This equation ties together pressure (\(P\)), volume (\(V\)), temperature (\(T\)) and the amount of substance in moles (\(n\)) with the ideal gas constant \(R\).

- **Boyle's Law:** States that pressure and volume are inversely proportional at constant temperature.\[ P \propto \frac{1}{V} \]
- **Charles's Law:** Relates volume and temperature, asserting that volume is directly proportional to temperature at constant pressure.\[ V \propto T \]
- **Avogadro's Law:** Establishes that volume is directly proportional to the number of moles at constant temperature and pressure.\[ V \propto n \]

Using the Ideal Gas Law, you can rearrange variables to find missing information about a gas sample. For our exercise, it was critical to solve for concentration, and by reorganizing the equation \( PV = nRT \), we found \( \frac{n}{V} = \frac{P}{RT} \), adhering to the option (a) solution.

Concentration of Solutions

Concentration measures how much solute is present in a solution relative to the amount of solvent. For gases, concentration is often measured in moles per liter (\( \text{mol/L} \)), making it crucial in understanding the behavior of gases in different conditions.

The formula \( \text{concentration = } \frac{n}{V} \) helps express this idea, where \(n\) is the number of moles and \(V\) is the volume in liters.

- **Dilute Solutions:** Low concentration; fewer moles of solute.
- **Concentrated Solutions:** High concentration; more moles of solute.

When dealing with the Ideal Gas Law, solving for concentration shows how pressure, volume, and temperature contribute to the concentration of a gas. By rearranging \( PV = nRT \) to obtain \( \frac{n}{V} = \frac{P}{RT} \), we derive a practical method for estimating a gas’s concentration given its volume, pressure, and temperature.
This process directly reflects in the exercise solution with option (a), linking the gas laws to a practical concentration calculation.